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A067142 One half of the number of Young tableaux with n cells whose shape is asymmetric. 2
0, 0, 1, 1, 4, 10, 30, 106, 316, 1254, 4140, 17128, 63856, 271492, 1126216, 4936608, 22278712, 101330506, 487735440, 2313734596, 11706759352, 58073844300, 305941244576, 1587272257096, 8656011151184, 46886237603400, 263791190603200, 1487539434072976 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Equivalently, the row lengths are a non-self-conjugate partition of n.

LINKS

Table of n, a(n) for n=0..27.

FORMULA

a(n) = (A000085(n) - A067136(n))/2.

a(n) = A330645(n)/2. - Omar E. Pol, Jan 11 2020

EXAMPLE

a(4) = 4 = 8/2; the 8 tableaux are:

1..1234..123..124..134..14..12..13

2........4....3....2....2...3...2.

3.......................3...4...4.

4.................................

The two tableaux of size 4 with symmetric shape are excluded:

12..13

34..24

CROSSREFS

Cf. A000085, A000700, A000701, A067136, A330645.

Sequence in context: A114946 A243793 A001551 * A145453 A346754 A333916

Adjacent sequences: A067139 A067140 A067141 * A067143 A067144 A067145

KEYWORD

nonn

AUTHOR

Naohiro Nomoto, Feb 19 2002

EXTENSIONS

Edited by Franklin T. Adams-Watters, Nov 07 2006

a(26)-a(27) from Omar E. Pol, Jan 11 2020

STATUS

approved

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Last modified February 7 22:58 EST 2023. Contains 360132 sequences. (Running on oeis4.)